Bayesian estimation of inverse burr stress-strength model for power system components reliability assessment

Abstract

A novel Inverse Burr stress-strength probabilistic model is proposed for reliability assessment of electrical components in the presence of overstresses, such as extreme wind-speed values for wind towers reliability modeling or extreme voltage surge amplitudes for insulation reliability modeling. These are kinds of stresses which can be modeled by means of adequate, well-known extreme value distributions, such as Gumbel and Inverse Weibull distributions. However, Inverse Burr models have also been recently proven to be efficient and flexible extreme values models. In this paper, also the “strength” of electrical components is characterized through an Inverse Burr distribution. The estimation of the overall reliability of the component is performed through classical Maximum Likelihood Estimation procedure and through a new proposed Bayesian methodology, based upon the assessment of prior distributions on given parameters of the stress and strength distributions. Indeed, usually only a limited amount of lifetime data are available for high-reliability electrical components, while data on strengths or stresses are easier to get. Therefore, the application of a Bayesian approach is particularly appropriate in situations characterized, on one hand, by lack of experimental data, and, on the other hand, by some degree of technical knowledge. The validation of the stress-strength model and the comparison between both reliability estimation methods is confirmed through a numerical application, considering typical values of reliability of electrical components. The results proved the usefulness of the Bayesian reliability estimation procedure and the feasibility of the Inverse Burr stress-strength model.